Problem: Express this product in scientific notation: $(9.70\times 10^{3})\times (4.00\times 10^{4})$
Solution: Start by collecting like terms together. $= (9.70\times 4.00) \times (10^{3}\times 10^{4})$ When multiplying exponents with the same base, add the powers together. $= 38.8 \times 10^{3\,+\,4}$ $= 38.8 \times 10^{7}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $38.8$ is the same as $3.880 \times 10$ $ = {3.880 \times 10} \times 10^{7} $ $= 3.880\times 10^{8}$